In the oil and gas industry, modeling of the subsurface is typically utilized for visualization and to assist with analyzing the subsurface volume for potential locations for hydrocarbon resources. Accordingly, various methods exist for estimating the geophysical properties of the subsurface volume (e.g., information in the model domain) by analyzing the recorded measurements from receivers (e.g., information in the data domain) provided that these measured data travel from a source, then penetrate the subsurface volume represented by a subsurface model in model domain, and eventually arrive at the receivers. The measured data carries some information of the geophysical properties that may be utilized to generate the subsurface model.
To generate subsurface models, labels may be applied to the different surfaces within the model. For example, automatically extracting depositional surfaces is particularly useful in seismic data interpretation. Such a process automates the generation of so-called Wheeler diagrams, which provide insights that are difficult to obtain otherwise. Various methods have been proposed in the literature to provide certain aspects of this approach. For example, U.S. Pat. No. 6,850,845 to Stark describes a method to compute seismic horizons and arrange them in a geologic time volume. This method describes phase unwrapping as a mechanism to compute this volume and the horizons. However, the method is computationally expensive, which is further compounded by larger data sets.
Another approach that may be utilized is described in U.S. Pat. No. 7,769,546 to Lomask et al. and a paper entitled “Flattening without picking”, Geophysics 71, 13-20 (2006). This method describes a global optimization approach that computes a flattened volume from which surfaces may be extracted, wherein the horizon locations are determined for each time slice. This method may require the creation of a volume several times the size of the original volume and, as the method is iterative, it may require multiple iterations for complex data. As a result, the method involves large data amounts and is computationally expensive.
As yet another example of another approach, a publication by Fomel (entitled “Predictive painting of 3-D seismic volumes”, SEG 2008, pp. 864-868) describes a prediction principle to propagate surfaces. This method uses plane-wave destruction to compute a prediction operator Pij that predicts the seismic character (i.e. amplitudes) of trace j given a character at trace i. This computation is a global optimization problem whereby it seeks to minimize the prediction error for all pairs of nearby traces. The resulting operators Pij may then carry any number through, including labels. However, a trace is predicted by only one trace preceding it and the local dip cannot be adjusted because the method relies upon the plane-wave destruction computation. As such, this method may tend to have poor behavior in noisy areas. Further, similar to the other methods, the optimization problem may be computationally expensive for large number of traces (e.g. 3-D volumes).
Another approach that may be utilized is described in an OpendTect's publication. See OpendTect's dGB plugin (user manual: http://www.opendtect.org/rel/doc/User/dgb/chapter3.4_horizoncube_creator.htm#LINK-HORIZONCUBE. CREATOR, dated Oct. 18, 2012). This document describes a method that follows a local dip field to define line segments in 2-D and surface patches in 3-D. In this method, an automated decision is made as to which surfaces at an intersection are to terminate and which surface is to continue. When the empty space between two surfaces exceeds a threshold, then a new surface is introduced. The result of this method is a finite number of surface patches. However, this approach provides surfaces that are not dense and have gaps that are user-controlled, and the surfaces may be difficult to adjust.
Yet another approach that may be utilized is described in a publication by Dave Hale. See Hale, entitled “Image-guided blended neighbor interpolation”, Center for Wave Phenomena report 634, also abstract in SEG2009: 79th Annual Meeting Society of Exploration Geophysicists. This method describes interpolating labels (numbers) from a set of points to the remaining portions of the data cube. The method describes the use of different diffusion methods, such as harmonic or biharmonic interpolation. This method consists of two key steps: (1) compute a distance map (modified by local tensor measurements of the seismic data), and (2) interpolate along this distance. This method may be slow because it needs to perform multiple iterations to solve the partial differential equation that describes harmonic or biharmonic interpolation (e.g., iterations are proportional to one dimension of the data). Accordingly, this method is inefficient and the multiple iterations further complicate the inefficiencies.
As the recovery of natural resources, such as hydrocarbons, rely, in part, on subsurface model, a need exists to enhance subsurface models of one or more geophysical properties. In particular, a need exists for a locally adaptive method, which utilizes any vector field as input, including vectors obtained by this method. Further, a need exists for a method to produce surfaces that span the whole areal extent of the volume and provide surfaces at every location of the volume (e.g., a dense set of surfaces).
What is needed is process that provides a dense set of surfaces that can be adjusted through user interaction, that enhances the representations of geologic features, such as geo-bodies, and that provides a dense representation of surfaces of at least one per voxel.